Sharp upper-bound conjecture for Fermat quotients

Let $v_p$ denote the $p$-adic valuation. The variables $x$ and $q$ are integers with $x>1$, and $p$ and $q$ are primes in the second assertion. Sharp upper-bound conjecture for Fermat quotients. Except for finitely many pairs $(x,p)$, one has

$$v_p(x^{p-1}-1)\leq 2+\frac{\log x+2\log\log x+\log\log p}{\log p}.$$

Furthermore, except for finitely many pairs $(q,p)$ of primes, one has

$$v_p(q^{p-1}-1)\leq 2+\frac{\log q+\log\log q+\log\log p}{\log p}.$$

The conjecture is presented as a sharper form of the preceding bounds; the source also notes a consequence under the abc conjecture, but does not establish these assertions.